• # question_answer If a spring of stiffness 'k' is cut into two parts 'A' and 'B' of length ${{\ell }_{A}}:{{\ell }_{B}}=2:3,$then the stiffness of spring 'A' is given by:   [AIEEE 11-05-2011]     A) $\frac{3k}{5}$ B) $\frac{2k}{5}$ C) $k$ D) $\frac{5}{2k}$

 [d] ${{\ell }_{A}}=\frac{2\ell }{5},{{\ell }_{B}}=\left( \frac{3\ell }{5} \right)$ $K\ell ={{K}_{A}}{{\ell }_{B}}={{K}_{B}}{{\ell }_{B}}$ $K\ell ={{K}_{A}}\left( \frac{2\ell }{5} \right)$ ${{K}_{A}}=\frac{5K}{2}$ $\Rightarrow$${{K}_{B}}=\frac{5K}{3}.$